Steel Beam Calculator

Design a simply-supported W-shape beam — given load, span, steel grade and deflection limit, pick the smallest AISC section that satisfies both bending stress and deflection.

Beam & load

ft
lb/ft
UDL in lb/ft of beam length (service load, unfactored).

Steel & deflection

F_b = 0.60·F_y is the conservative ASD bending allowable.
Span divided by this number = max allowable midspan deflection.

Calculation results

Recommended W-shape

—

Maximum moment (M_max)

— kip·ft

Required Sₓ

— in³

Allowable bending stress F_b

— ksi

Allowable deflection

— in

Actual deflection (recommended shape)

— in

The recommended shape is the lightest W-section that satisfies both bending (Sₓ ≥ required) and deflection (actual ≤ allowable). E = 29,000 ksi for structural steel. Service load is unfactored — for LRFD, factor by 1.2D + 1.6L before entering.

Informational only. Lateral-torsional buckling, compact-section check, shear, web crippling, bearing and connection design are NOT included. For any structural beam in real construction, a licensed engineer must perform the full check per AISC 360.

Beam sizing formulas

UDL: Mmax = w·L² / 8  ·  δmax = 5·w·L⁴ / (384·E·I)
Point at centre: Mmax = P·L / 4  ·  δmax = P·L³ / (48·E·I)
Required Sₓ = Mmax / Fb  ·  Fb = ratio × Fy

The calculator iterates the AISC W-shape table by Sₓ (ascending), picks the first shape with Sₓ ≥ required, then verifies the chosen Iₓ also satisfies the deflection limit. If deflection governs, it steps up to a larger shape.

Worked example — 20 ft span, 1,000 lb/ft UDL, A992, L/360

  • w = 1,000 lb/ft = 1.0 kip/ft
  • Mmax = 1.0 × 20² / 8 = 50 kip·ft = 600 kip·in
  • Fb = 0.60 × 50 ksi = 30 ksi
  • Required Sₓ = 600 / 30 = 20 in³
  • Smallest W-shape with Sₓ ≥ 20 in³: W12×16 (Sₓ = 17.1)? — too small; W12×26 (Sₓ = 33.4) — passes
  • Allowable δ = 20 × 12 / 360 = 0.667 in
  • Actual δ for W12×26 (I = 204 in⁴): δ = 5 × 1 × 240⁴ / (384 × 29,000 × 204) = 0.292 in ✓

Frequently asked questions

What size steel beam for a 20 foot span?
Depends on load. For a typical residential UDL of 500 lb/ft on a 20 ft simply-supported span (A992, L/360), the required Sx is about 10 in³ — W8×10 fits but check deflection. For 1,000 lb/ft UDL the required Sx is ~20 in³ — go to W12×26.
What is the maximum span for a W8 beam?
For a W8×10 (Sx = 7.81 in³) with A992 steel and 30 ksi allowable bending: M_max = 19.5 kip·ft. At 500 lb/ft UDL, that corresponds to L² = 19.5×8/0.5 → L ≈ 17.7 ft. At lower loads (200 lb/ft), span extends to ~27 ft. Deflection often governs before stress on long spans.
A36 or A992 steel — which to use?
A992 (F_y = 50 ksi) has been the U.S. residential and commercial standard since 1998. A36 (F_y = 36 ksi) is essentially obsolete for new construction wide-flange shapes — it is still made for plates and angles but rarely seen in modern beams. Use A992 unless your supplier confirms otherwise.
What is the deflection limit for a steel beam?
L/360 for floor live load (preferred) or L/240 (minimum code). For roofs, L/240 is the live-load minimum. For vibration-sensitive spaces (gyms, dance studios) use L/480 or stricter. A 20-ft span at L/360 allows 0.67 in of deflection at midspan.
How do I calculate beam load capacity?
Inverse problem: given the beam, find the max load. Use our Beam Load Calculator for that direction. This Steel Beam Calculator goes from load+span → beam size; Beam Load goes from beam+span → max load.
Does this calculator check lateral-torsional buckling?
No. The calculator assumes the beam is fully laterally braced (continuous floor diaphragm above, for example). For beams supporting unbraced lengths beyond Lp from AISC 360 Table 3-2, the bending capacity reduces — a licensed engineer must verify.
What is the section modulus Sx?
Section modulus is I / c, where I is moment of inertia and c is the distance from the centroid to the extreme fiber. It directly relates moment to bending stress: σ = M / S. We tabulate Sx for every standard W-shape from AISC Manual.